The rectangle is divided into four parts D, E, F and G. The ratio of Part D to Part E is 10 : 3 and the ratio of Part E to Part F is 3 : 2.
- Find the ratio of Part D to Part E to Part F.
- Given that Part G is 66 cm2 , find the area of the rectangle.
(a)
D |
E |
F |
G |
10x1 |
3x1 |
|
|
|
3x1 |
2x1 |
|
10 u |
3 u |
2 u |
66 cm2 |
Part E is the repeated identity.
LCM of 3 and 3 = 3
Part D : Part E : Part F = 10 : 3 : 2
(b)
Part D + Part E = Half of the rectangle
Part F + Part G = Half of the rectangle
Part D + Part E and Part F + Part G are equal.
Part D + Part E = Part F + Part G
10 u + 3 u = 2 u + 66
10 u + 3 u - 2 u = 66
11 u = 66
1 u = 66 ÷ 11 = 6
Area of the rectangle
= 2 x (2 u + 66)
= 2 x (2 x 6 + 66)
= 2 x (12 + 66)
= 2 x 78
= 156 cm
2 Answer(s): (a) 10 : 3 : 2; (b) 156 cm
2